Topological phase in a non-Hermitian <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi mathvariant="script">PT</mml:mi></mml:math> symmetric system

Yüce, C.

doi:10.1016/j.physleta.2015.02.011

Cited by 130 publications

(46 citation statements)

References 28 publications

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“…A direct implication of this result is the interface state formed by two PCs with different topological invariants. Recently, interface states in some non-Hermitian systems have been reported [47][48][49]. It is known that for Hermitian systems there is a rigorous mathematical relationship that connects the quantized Zak phase of the bulk bands with the formation of interface states [44].…”

Section: Band Inversion In 1d Pt -Symmetric Pcmentioning

confidence: 99%

Coalescence of exceptional points and phase diagrams for one-dimensionalPT-symmetric photonic crystals

2015

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Non-Hermitian systems with parity-time-(PT )-symmetric complex potentials can exhibit a phase transition when the degree of non-Hermiticity is increased. Two eigenstates coalesce at a transition point, which is known as the exceptional point (EP) for a discrete spectrum and spectral singularity for a continuous spectrum. The existence of an EP is known to give rise to a great variety of novel behaviors in various fields of physics. In this work, we study the complex band structures of one-dimensional photonic crystals with PT -symmetric complex potentials by setting up a Hamiltonian using the Bloch states of the photonic crystal without loss or gain as a basis. As a function of the degree of non-Hermiticity, two types of PT symmetry transitions are found. One is that a PT -broken phase can reenter into a PT -exact phase at a higher degree of non-Hermiticity. The other is that two EPs, one originating from the Brillouin zone center and the other from the Brillouin zone boundary, can coalesce at some k point in the interior of the Brillouin zone and create a singularity of higher order. Furthermore, we can induce a band inversion by tuning the filling ratio of the photonic crystal, and we find that the geometric phases of the bands before and after the inversion are independent of the amount of non-Hermiticity as long as the PT -exact phase is not broken. The standard concept of topological transition can hence be extended to non-Hermitian systems.

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Section: Band Inversion In 1d Pt -Symmetric Pcmentioning

confidence: 99%

Coalescence of exceptional points and phase diagrams for one-dimensionalPT-symmetric photonic crystals

2015

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“…Based on these fun- * Electronic address: schen@aphy.iphy.ac.cn damental issues, the effects of the non-Hermitian terms have been investigated under different boundary conditions. Under the open boundary condition (OBC), the Bethe ansatz solution of a 1D tight-binding chain with two conjugated imaginary potentials at two end sites confirms the non-Hermitian PT -symmetric quantum theory for the discrete systems [17][18][19]. Under the periodic boundary condition (PBC), the topological invariance is derived to find the topological properties in the quantum evolution of non-Hermitian models [20].…”

Section: Introductionmentioning

confidence: 63%

“…While the PT -symmetry breaking in the eigenvalue problem of non-Hermitian lattice model has been extensively studied [17][18][19], the PT -symmetry breaking in the lattice scattering problem is not well understood yet. The study of the simple lattice model can illustrate the most fundamental principle in the non-Hermitian scattering process and helps us to understand the more complicated phenomenon in other models.…”

Section: Introductionmentioning

confidence: 99%

PT-symmetry breaking for the scattering problem in a one-dimensional non-Hermitian lattice model

2016

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We study the PT -symmetry breaking for the scattering problem in a one-dimensional (1D) nonHermitian tight-binding lattice model with balanced gain and loss distributed on two adjacent sites. In the scattering process the system undergoes a transition from the exact PT -symmetry phase to the phase with spontaneously breaking PT -symmetry as the amplitude of complex potentials increases. Using the S-matrix method, we derive an exact discriminant, which can be used to distinguish different symmetry phases, and analytically determine the exceptional point for the symmetry breaking. In the PT -symmetry breaking region, we also confirm the appearance of the unique feature, i.e., the coherent perfect absorption Laser, in this simple non-Hermitian lattice model. The study of the scattering problem of such a simple model provides an additional way to unveil the physical effect of non-Hermitian PT -symmetric potentials.

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“…Fortunately, a few years ago, stable topological phase was shown to exist in a non-Hermitian symmetric system, where and are parity and time reversal operators, respectively 6,7 . In 6 , it was theoretically predicted that stable topological phase is compatible in a non-Hermitian Aubry-Andre model 6 . A topological zero energy state was observed through fluorescence microscopy in a lattice of waveguides with staggered hopping amplitudes 7 .…”

Section: Introductionmentioning

confidence: 99%